Does a rotating ring of uniform charge constitute a current?

If I have a charged insulating hula-hoop with the property that every point on the ring has exactly the same charge per volume as every other point on the ring, and I spin it around its axis, does that produce a current?

If I consider a "window" cutting through some part of the ring, I will see charge carriers moving through that window, so I'd think there is a current.

But if I consider any segment of the ring of infinitesimal length, dQ/dt = 0 at all times, so I'd think there is not a current.

It is a current and will result in a magnetic field. Current is the flow of charge in space.

Well, why? The current density flux through any closed surface on the ring is always zero, and that should be equal to the current.

From the perspective of Ampere's law, I would think there would be a current, because charges will cross an open surface that cuts the ring. But from the perspective of the current density, I would think there is not a current. Why is one answer wrong?

Staff: Mentor

Well, why? The current density flux through any closed surface on the ring is always zero, and that should be equal to the current.

No, in this case a closed surface on the ring is moving, you cannot use a moving surface to determine a current. Let's consider an absurd example to demonstrate the point. Let's say that you have a wire with only positive charge carriers moving at exactly 1 m/s. This is clearly a current. Now lets make a surface that also moves at 1 m/s, no net flux through it. According to your logic that would eliminate the current. That is why you cannot use a moving surface to determine current.

But if I consider any segment of the ring of infinitesimal length, dQ/dt = 0 at all times, so I'd think there is not a current.

I don't think a current is necessarily given by dQ/dt. Consider the case of a circular loop with a current induced by a magnet being drawn through its center. The system is symmetric, so charge should be constant around the loop.

Current does not need a change in total charge to take place. Change in charge or charge density will lead to a divergence, source or sink, of current. But current can flow and even increase or decrease without charge building up.

Charge and current are sometimes separate in classical electro magnetics.

To answer the original question, not only are charges moving in the circular system, they are accelerating. There is a current, and a magnetic field will be generated. In fact, the system you describe is perhaps akin to charged plasma in a tokamak.

If I have a charged insulating hula-hoop with the property that every point on the ring has exactly the same charge per volume as every other point on the ring, and I spin it around its axis, does that produce a current?

If I consider a "window" cutting through some part of the ring, I will see charge carriers moving through that window, so I'd think there is a current.

But if I consider any segment of the ring of infinitesimal length, dQ/dt = 0 at all times, so I'd think there is not a current.

Which is right?

You can sense (or measure) the magnetic field by holding a compass near your rotating, charged hoop. But, if you mount the compass on the moving hoop, the dipoles of the compass needle will be moving and generate an electric field that interacts with the electric field of the hoop. This interaction will cancel any torque on the compass.

The answer is yes, a rotating charged ring does constitute an electrical current in the laboratory (nonrotating) frame -- this kind of electric current is called a convection current --anytime you have bare charges moving relative to the observer (as in this case) there is an electrical current called a convection current and i does produce a magnetic field.

The answer is yes, a rotating charged ring does constitute an electrical current in the laboratory (nonrotating) frame -- this kind of electric current is called a convection current --anytime you have bare charges moving relative to the observer (as in this case) there is an electrical current called a convection current and i does produce a magnetic field.

Another example of a convection current is the electron beam in a cathode ray tube.

By the way, the typical kind of electric current that you have in an electical wire in which electrons move through the copper conductor is called a conduction current.